My only disagreement with Mr. Pitts is in seeing action. If Morrow joined in late March or early April, 1862, he very well may have seen action at:
Corinth Campaign [April-June 1862]
Round Hill, on Cache River [July 7, 1862]
Had he then been discharged at Little Rock, Arkansas on July 17, 1862, that would have been the extent of him seeing action.

In additon to what Mr. Pitts has said, the Compendiium of The Confederate Armies - Texas - by Stewart Sifakis, pages 74-75, shows:

Texas 17th Cavalry Regiment
Organization: Organized in early 1862 - Dismounted in April 1862 - surrendered at Arkansas Post on January 11, 1863 - Exchanged in April 1863 - Field Consolidation with the 18th Texas Cavalry Regiment from July 1863 to April 9, 1865 - Additional filed consolidations with the 24th and 25th Texas Cavalry Regiments from July 1864 to April 9, 1865 - Consolidated with the 6th, 7th, and 10th Infantry Regiments and the 15th, 18th, 24th, and 25th Cavalry Regiments (Dismounted) and designated as the 1st Infantry Regiment Consolidated at Smithfield, North Carolina on April 9, 1865.
First Commander: George F. Moore [Colonel]
Field Officers: Sterling B. Hendricks [Lt Colonel]
John McClarty [Major]
Sebron M. Noble [Major, Lt Col]
James R. Taylor [Colonel]
Thomas F. Tucker [Major, Colonel]
Assignments: Eastaern District of Texas, Department of Texas [March 1862]
Rust's-Parsons' Cavalry Brigade, Trans-Mississippi District, Department #2 [March-April 1862]
3rd Brigade, McCown's Division, Army of the West, Department #2 [April-June 1862]
Trans-Mississippi Department [June-August 1862]
Districts of Arkansas, Trans-Mississippi Department [August-September 1862]
Sweet's Brigade, Nelson's Division, District of Arkansas, Trans-Mississippi Department [September 1862]
Nelson's-Deshler's Brigade, Nelson's-Churchill's Division, 2nd corps, Trans-Mississippi Department [September-December 1862]
Deshler's Brigade, Churchill's Division, District of Arkansas, Trans-Mississippi Department [December 1862-January 1863]
Churchill's-Deshler's-Smith's Brigade, Cleburn's Division, 2nd Corps, Army of Tennessee [May-November 1863]
Smith's-Granbury's Brigade, Cleburn's Division, 1st corps, Army of Tennessee [November 1863-April 1865]
Battles: Corinth Campaign [April-June 1862]
Round Hill, on Cache River [July 7, 1862]
Arkansas Post {January 4-11, 1863]
Fayetteville [April 18, 1863] [Detachment]
Chickamauga [September 19-20, 1863]
Chattanooga Siege [September-November 1863]
Chattanooga [November 23-25, 1863]
Atlanta Campaign [May-September 1864]
Pickett's Mill [May 27, 1864]
New Hope Church [ June 27, 1864]
Atlanta Siege [July-September 1864]
Jonesboro [August 31 - September 1, 1864]
Franklin [November 30, 1864]
Nashville [December 15-16, 1864]
Carolinas Campaign [February-April 1865]
Bentonville [March 19-21, 1865]